Computable Analysis: An Introduction

Front Cover
Springer Science & Business Media, Dec 6, 2012 - Computers - 288 pages
Is the exponential function computable? Are union and intersection of closed subsets of the real plane computable? Are differentiation and integration computable operators? Is zero finding for complex polynomials computable? Is the Mandelbrot set decidable? And in case of computability, what is the computational complexity? Computable analysis supplies exact definitions for these and many other similar questions and tries to solve them. - Merging fundamental concepts of analysis and recursion theory to a new exciting theory, this book provides a solid basis for studying various aspects of computability and complexity in analysis. It is the result of an introductory course given for several years and is written in a style suitable for graduate-level and senior students in computer science and mathematics. Many examples illustrate the new concepts while numerous exercises of varying difficulty extend the material and stimulate readers to work actively on the text.
 

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Contents

Introduction
1
Computability on the Cantor Space
13
Naming Systems 51
50
Computability on the Real Numbers
85
Computability on Closed Open and Compact Sets
123
Spaces of Continuous Functions
153
Computational Complexity
195
Some Extensions
237
Other Approaches to Computable Analysis
249
References
269
Index
277
Copyright

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